DSpace at VNU: Critical behavior of La0.7Ca0.3Mn1 x NixO3manganites exhibiting the crossover offirst- and second-order phase transitions

Solid State Communications 184 (2014) 40–46

Contents lists available at ScienceDirect

Solid State Communications
journal homepage: www.elsevier.com/locate/ssc

Critical behavior of La0.7Ca0.3Mn1 À xNixO3 manganites exhibiting the
crossover of first- and second-order phase transitions
The-Long Phan a, Q.T. Tran b, P.Q. Thanh c, P.D.H. Yen d, T.D. Thanh a,e, S.C. Yu a,n
a

Department of Physics, Chungbuk National University, Cheongju 361-763, South Korea
Center for Science and Technology Communication, Ministry of Science and Technology, 113 Tran Duy Hung, Hanoi, Vietnam
c
Faculty of Physics, Hanoi University of Science, Vietnam National University, Hanoi, Vietnam
d
Faculty of Engineering Physics and Nanotechnology, VNU – University of Engineering and Technology, Xuan Thuy, Cau Giay, Hanoi, Vietnam
e
Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
b

art ic l e i nf o

a b s t r a c t

Article history:
Received 29 October 2013
Received in revised form
28 December 2013
Accepted 29 December 2013

by F. Peeters
Available online 4 January 2014

We used Banerjee0 s criteria, modified Arrott plots, and the scaling hypothesis to analyze magneticfield dependences of magnetization near the ferromagnetic–paramagnetic (FM–PM) phasetransition temperature (T C) of perovskite-type manganites La0.7Ca 0.3Mn1 À xNixO 3 (x ¼0.09, 0.12 and
0.15). In the FM region, experimental results for the critical exponent β ( ¼0.171 and 0.262 for
x ¼ 0.09 and 0.12, respectively) reveal two first samples exhibiting tricriticality associated with the
crossover of first- and second-order phase transitions. Increasing Ni-doping content leads to the
shift of the β value ( ¼0.320 for x ¼ 0.15) towards that expected for the 3D Ising model (β ¼0.325).
This is due to the fact that the substitution of Ni ions into the Mn site changes structural parameters
and dilutes the FM phase, which act as fluctuations and influence the FM-interaction strength of
double-exchange Mn3 þ –Mn4 þ pairs, and the phase-transition type. For the critical exponent γ
( ¼0.976–0.990), the stability in its value demonstrates the PM behavior above T C of the samples.
Particularly, around T C of La0.7Ca 0.3Mn1 À xNixO 3 compounds, magnetic-field dependences of the
maximum magnetic-entropy change can be described by a power law of |Δ Smax| p H n, where values
n ¼ 0.55–0.77 are quite far from those (n ¼ 0.33–0.48) calculated from the theoretical relation n ¼1 þ
(β À 1)/(β þ γ). This difference is related to the use of the mean-field theory for the samples
exhibiting the magnetic inhomogeneity.
& 2014 Elsevier Ltd. All rights reserved.

Keywords:
A. Perovskite manganites
D. Critical behavior
D. Magnetic entropy change

1. Introduction
It is known that hole-doped lanthanum manganites of
La1 À x (Ca, Sr, Ba)xMnO 3 with x ¼0.3 (corresponding to Mn3 þ /
Mn4 þ ¼ 7/3) usually exhibit colossal magnetoresistance (MR)
and magnetocaloric (MC) effects around their the ferromagnetic–paramagnetic (FM–PM) phase-transition temperature
(the Curie temperature, T C) [1]. With this doping content,

double-exchange (DE) FM interactions between Mn3 þ and
Mn4 þ are dominant as comparing with super-exchange antiFM interactions of Mn3 þ –Mn3 þ and Mn4 þ –Mn4 þ pairs. The
strength of magnetic interactions thus depends on the average
bond length 〈Mn–O〉, and bond angle 〈Mn–O–Mn〉 of the
perosvkite structure. Different compounds have different bond
parameters, which are related to Jahn–Teller lattice distortions
due to strong electron–phonon coupling [2]. In reference to the

n

Corresponding author. Tel.: þ 82 43 261 2269; fax: þ 82 43 275 6416.
E-mail address: (S.C. Yu).

0038-1098/$ - see front matter & 2014 Elsevier Ltd. All rights reserved.
/>
symmetry of MnO 6 octahedra, it has been noted that cooperative Jahn–Teller distortions are present in an orthorhombic
structure rather than in the rhombohedral one [3].
Among hole-doped manganites, orthorhombic La0.7 Ca 0.3MnO3 is known as a typical material exhibiting MR and MC
effects much greater than those obtained from the other
compounds. Particularly, depending on bulk or nanostructured
sample types, its T C in the range of 222–265 K [3–9] can be
tuned towards room temperature by doping Sr, Ba or Pb [10–
14]. Meanwhile, the transition-metal doping (such as Co, Fe, Ni
and so forth) lowers TC [15–17]. Additionally, its discontinuous
FM–PM transition at T C is followed up with structural changes,
and is known as a first-order magnetic phase transition (FOMT)
[8,9,12]. This discontinuous phase transition can be rounded to
a continuous one of a second-order magnetic phase transition
(SOMT) upon the doping, and reduced dimensionality (i.e.,
finite-size effects), and external fields [5,7,11,12,16,18,19]. The

assessment of a continuous SOMT can base on the success in
determining the critical exponents β , γ , and δ associated with
temperature dependences of the spontaneous magnetization,


2. Experimental details
Three polycrystalline perovskite-type manganites La0.7 Ca0.3
Mn1 À x Nix O3 with x ¼0.09, 0.12 and 0.15 were prepared by solidstate reaction as using purity commercial powders La2 O3, CaO,
NiO, and MnCO 3 (99.9%) as precursors. These powders combined with stoichiometrical quantities were well mixed and
ground, and then pre-annealed at 900 1C for 24 h. After preannealing, three mixtures were re-ground and pressed into
pellets, and annealed at 1300 1C for 72 h in air. For reference,
the parent compound La0.7 Ca 0.3MnO3 was also prepared with
the same conditions as described. X-ray diffraction (XRD)
patterns of the final products checked by an X-ray diffractometer (Bruker AXS, D8 Discover) revealed the single phase in
an orthorhombic structure (the space group Pbnm) of
La 0.7Ca0.3 Mn1 À xNixO3 samples, see Fig. 1(a). Basing on the
XRD data, we calculated the lattice parameters (a, b, and c)
and unit cell (V), as shown in Table 1. The variation of these
parameters indicates the substitution of Ni ions (could be
Ni 2 þ , Ni 3 þ , and/or Ni4 þ ) for Mn in the perovskite structure.
Magnetic measurements were performed on a superconducting
quantum interference device magnetometer (SQUID). The TC
values obtained from the flexion points in temperature dependences of magnetization, M(T), with the applied field
H ¼ 100 Oe, Fig. 1(b) are about 200, 185 and 170 K for x ¼0.09,
0.12 and 0.15, respectively, which are lower than the value
TC E 260 K of the parent compound.

3. Results and discussion
Fig. 2 shows M–H data and inverse Arrott plots (H/M versus
M2 ) at different temperatures around the FM–PM phase transition of La 0.7Ca0.3 Mn1 À xNixO 3. It appears from the M–H data that

there is no saturation magnetization value in spite of the H
variation up to 40 kOe. This is assigned to the existence of the
magnetic inhomogeneity or short-range FM order. At a given
temperature, higher Ni-doping content reduces the magnetization. With increasing temperature, nonlinear M–H curves in the
FM region become linear because the samples enter the PM
state. Different from the parent compound [5,7–9,12], there is

(004)/(242)

(123)/(321)

(202)/(040)

(022)/(220)

Intensity (arb. units)

x = 0.15
x = 0.12
x = 0.09
x=0

30

40

50

60

70

2θ (degree)
1.2
H = 100 Oe

0.9

Normalized M

Ms(T), inverse initial susceptibility, χ 0 –1 (T), and critical isotherm
at TC, respectively [20,21]. Distinguishing the FOMT from the
SOMT can be based on the criteria proposed by Banerjee [22],
who performed H/M versus M2 curves (where H is the field, and
M is the magnetization) in the vicinity of T C, and then suggested
that their positive or negative slopes are indication of a secondor first-order phase transition, respectively.
Reviewing previous studies, one can see that many works
focused on La0.7Ca0.3 MnO3-based materials showing the FOMT
and/or SOMT. However, the crossover region from first-order to
second-order phase transitions, and some related physical
properties, such as the magnetic entropy change versus T and
H, ΔS m(T, H), have not been widely studied. Furthermore, there
is no much attention given to the assessment of a magnetic
ordering parameter (n) determined from the relations n ¼ 1 þ
(β À1)/(β þ γ ) [23], and from a power law |Δ Smax(H)| p Hn [24]
(where |Δ Smax| is the maximum magnetic entropy change
around TC). To get more insight into the above problems, we
prepared La0.7Ca0.3 Mn1 À xNi xO3 compounds, and have studied
their critical behaviors upon Banerjee0 s criteria [22], modified
Arrott plots and the scaling hypothesis [20,21]. The determined

critical values are then discussed together with the magnetic
ordering parameter n.

41

(121)

T.-L. Phan et al. / Solid State Communications 184 (2014) 40–46

x=0
x = 0.12

x = 0.09
x = 0.15

0.6

0.3

0.0
0

50

100

150

200

250

300

T (K)
Fig. 1. (Color online) (a) Room-temperature XRD patterns, and (b) normalized M(T)
curves with the applied field of H¼100 Oe for La0.7Ca0.3Mn1 À xNixO3 (x ¼0, 0.09,
0.12, and 0.15).

Table 1
Values of the lattice parameters and unit cell calculated from XRD analyses of
La0.7Ca0.3Mn1 À xNixO3 with x¼ 0.09, 0.12 and 0.15.
Sample, x

a (Å)

b (Å)

c (Å)

V (Å3)

0
0.09
0.12
0.15

5.473
5.467
5.461

5.474

4.461
5.451
5.450
5.450

7.711
7.707
7.719
7.713

230.46
229.70
229.73
230.10

no S-like shape in the M–H curves, and negative slopes in the H/
M versus M2 curves, see Fig. 2. These tokens demonstrate our
Ni-doped samples undergoing the FOMT [22,25].
According to the mean-field theory (MFT) proposed for a
ferromagnet exhibiting the SOMT and long-range FM interactions [26], the free energy GL is expanded in even powers of M:
GL ¼aM2 þbM4 þ⋯ – HM, where a and b are temperaturedependent parameters. Minimizing GL as ∂GL/∂M ¼0 results in
the relation H/M ¼2a þ 4bM2. It means that if magnetic interactions of the FM system exactly obey the MFT, M2 versus H/M
curves in the vicinity of TC are parallel straight lines. At TC, the
M2 and H/M line passes through the origin [27,28]. However,
these features are absent from the Arrott performance shown in
Fig. 2(b, d, and e). It means that magnetic interactions in the
samples could not be the long-range type. The critical exponents β ¼0.5 and γ ¼1.0 (in the normal Arrott plots [20,27])
based on the MFT are thus not suitable to describe magnetic

interactions taking place in our samples. Within the framework


42

T.-L. Phan et al. / Solid State Communications 184 (2014) 40–46

182 K

8

182 K

ΔT = 2 K

80
60

6
220 K

220 K

4

40

2

20

0

10

20

30

50

0

2

4

6

168 K

168 K

60

0

8

8

ΔT = 2 K

M (emu/g)

80

40

206 K

6

206 K

40

4

20

2

0

0

10

20

30

40

50

0

2

4

8

ΔT = 2 K

60

0

6

152 K

152 K

190 K

6

190 K

40

4

20
0

H/M (102, Oe.g/emu)

0

2

0

10

20
30
H (kOe)

40

50

0

1

2

3

4

5

0

M2 (103, emu/g)2

Fig. 2. (Color online) M–H data and inverse Arrott plots for La0.7Ca0.3Mn1 À xNixO3 with (a, b) x ¼0.09, (c, d) x¼ 0.12, and (e, f) x¼ 0.15.

of the MFT, we need to find other sets of the critical-exponent
values reflecting more frankly the magnetic properties of the
samples. This work is based on the modified Arrott plot (MAP)
method [20], which is generalized by the scaling equation of
γ
β
state, (H/M)1/ ¼c1 ε þ c2M1/ , where c1 and c2 are temperaturedependent parameters, and ε ¼(T À TC)/TC is the reduced temperature. β and γ values can be obtained from the asymptotic
relations [18,20]
M s ðTÞ ¼ M 0 ð À εÞβ ;

χ 0À 1 ðTÞ ¼ ðh0 =M0 Þεγ ;
M ¼ DH 1=δ ;

ε ¼ 0;

ε o 0;
ε 4 0;

ð1Þ
ð2Þ
ð3Þ

where M0, h0 , and D are the critical amplitudes. Additionally,
according to the static-scaling hypothesis [21], M is a function
of ε and H, MðH; εÞ ¼ jεjβ f 7 ðH=jεjβ þ γ Þ. This equation reflects
β
that, with determined β and γ values, plotting M/ε versus H/
εβ þ γ makes all data points falling on the f À and f þ branches for
T o TC and T 4 T C, respectively. Here, determining the critical
parameters is based on the MAP method, and started from the
scaling equation of state. Correct β and γ values make M–H data
points falling on a set of parallel straight lines in the

β

γ

β

performance of M1/ versus (H/M)1/ . Moreover, the M1/ versus
γ
(H/M)1/ line passes through the origin at T C. Similar to the MFT
case, our analyses indicated that the exponent values β ¼0.365
and γ ¼1.336 expected for the 3D Heisenberg model [21] do not
match with the descriptions of the MAP method. Only β ¼0.25

and γ ¼ 1.0 expected for the tricritical MFT model (T-MFT), and
β ¼0.325 and γ ¼1.241 expected for the 3D Ising model [12,29]
can be used as initially trial values to find optimal exponent
values for the samples with x ¼0.09 and 0.12, and for x ¼0.15,
respectively. With these trial values, Ms(T) and χ 0(T) data would
be obtained from the linear extrapolation in the high-field
β
region for the isotherms to the co-ordinate axes of M1/ and
1/ γ
1/ γ
(1/χ 0 ) ¼(H/M) , respectively. The Ms(T) and χ 0(T) data
obtained from the linear extrapolation are then fitted to Eqs.
(1) and (2), respectively, to achieve better β , γ and TC values, as
can be seen from Fig. 3. These new values of β , γ , and TC are
continuously used for next MAP processes until their optimal
values are achieved. Notably, the T C values of the samples
obtained from M–T measurements were also used as reference
in the fitting. With such the careful comparison, only the sets
of critical parameters with T C E 199.4 K, β ¼ 0.171 7 0.006 and
γ ¼ 0.976 7 0.012 for x ¼0.09; TC E 184.4 K, β ¼ 0.262 7 0.005 and
γ ¼ 0.979 7 0.012 for x ¼0.12; and TC E 170 K, β ¼0.320 7 0.009


T.-L. Phan et al. / Solid State Communications 184 (2014) 40–46

64
56

12

4

72

TC = 199.4 ± 0.3
γ = 0.976 ± 0.012

185

190

195

200

205

210

186 K

x = 0.09
β = 0.171
γ = 0.976

8

2
TC = 199.5 ± 0.1
β = 0.171 ± 0.006

43

4

0

214 K

215

40
30

2
TC = 184.3 ± 0.1
γ = 0.979 ± 0.012

TC = 184.5 ± 0.1
β = 0.262 ± 0.005

170

175

180

0
185

190

195

200
3

50

2

40

β = 0.320 ± 0.009

160

165

200

400

170

175

180

600

174 K

x = 0.12

30

β = 0.262
γ = 0.978

20

10

200 K

0
0

1

0.6

0
185

0.4

200

400

600

152 K

TC = 169.6 ± 0.5 K
γ = 0.990 ± 0.082

30 TC = 170.0 ± 0.1 K
155

0

M1/βx106 (emu/g)1/β

4

50

-1

Ms (emu/g)

60

χ0 (x102, Oe.g/emu)

0

800

x = 0.15
β = 0.320
γ = 0.990

T (K)
Fig. 3. (Color online) Ms(T) and χ 0À 1 ðTÞ data fitted to Eqs. (1) and (2) for
La0.7Ca0.3Mn1 À xNixO3 with (a) x¼ 0.09, (b) x ¼0.12, and (c) x¼ 0.15.

and γ ¼0.990 7 0.082 for x ¼0.15 are in good agreement with
the MAP descriptions, see Fig. 4. With the obtained critical
β
β γ
exponents, the scaling performance of M/|ε | versus H/ε þ
curves, see Fig. 5 and their inset, reveals the M–H data points at
high-magnetic fields falling into two f À and f þ universal
branches for T o TC and T 4 TC, respectively. These results prove
the reliability in value of the critical values obtained from our
work. It should be noticed that the MAP method only works
well for the fields (HL ) higher than 28, 24 and 12 kOe for
x ¼ 0.09, 0.12 and 0.15, respectively. At the fields lower than
HL , there may be rearrangement of magnetic domains, the effect
due to the uncertainty in the calculation of demagnetization
factor, and/or the persistence of the FOMT (particularly for the
samples with x ¼0.09 and 0.12) [12,30]. Unexpected errors for
critical values can thus be occurred, leading to the scattering of
the M–H data points (at the fields lower than H L) from the
universal curves [5,12], as can be seen in Fig. 5. For the
exponent δ , its value can be obtained from fitting the isotherms

at T ¼T C to Eq. (3). Basically, the δ values determined from Eq.
(3) would be equal to those calculated from the Widom relation
δ ¼ 1 þ γ/β [21]. In our work, δ values are about 6.7, 4.7, and
4.1 for x ¼0.09, 0.12 and 0.15, respectively. Clearly, with increasing Ni concentration in La 0.7Ca0.3 Mn1 À xNixO 3, there is a shifting
tendency of the exponent values (β , γ and δ ) towards those of
the MFT (with β ¼0.5, γ ¼ 1 and δ ¼3). This is tightly related to
the FOMT–SOMT transformation. The better applicability of the
MAP method has been found for the samples with high-enough
Ni concentrations as x 4 0.12. We believe that the substitution

180 K

0.2

0.0
0

200

400
(H/M)

1/γ

800

600
(Oe.g/emu)

1000

1/γ

Fig. 4. (Color online) MAPs of M1/β versus (H/M)1/γ with the critical exponents
obtained for La0.7Ca0.3Mn1 À xNixO3 with (a) x ¼0.09, (b) x ¼0.12 and (c) x¼ 0.15.

of Ni ions into the Mn site not only changes structural parameters of 〈Mn–O〉 and 〈Mn–O–Mn〉, but also leads to the
additional presence of anti-FM interactions related to Ni ions
(for example, super-exchange pairs of Ni 2 þ –Ni2 þ , Ni3 þ –Ni3 þ ,
Ni4 þ –Ni 4 þ , and/or Ni2 þ ,3 þ ,4 þ –Mn3 þ ,4 þ ) besides pre-existing
anti-FM interaction pairs of Mn3 þ –Mn3 þ and Mn4 þ –Mn4 þ .
These factors act as fluctuations, reduce the strength of
Mn3 þ –Mn4 þ FM interactions (which thus reduce the magnetization and TC values), and influence the phase transition
as well.
Comparing with the theoretical models [21,29], one can see
that the values of γ ( ¼0.976–0.990) are quite stable, demonstrating the complete PM state in the samples at temperatures
above TC. For the FM region, however, β ¼0.262 for x ¼0.12 is
close to that expected for the T-MFT (β ¼ 0.25). This sample thus
exhibits tricriticality associated with the crossover of first- and
second-order phase transitions. Similar results were also found
in some manganites [9,12,29]. A smaller value of β ¼ 0.171 for
x ¼0.09 reveals this sample lying in the region close to the
crossover, where the FOMT is still persistent. It is also known
that the MAP application for the materials with the presence


44

T.-L. Phan et al. / Solid State Communications 184 (2014) 40–46

T < TC

102

T < TC

M/|ε|β

150

101

100

T > TC

50
0

T > TC
100

104

105

106

107

T < TC

102

200

T < TC

150
M/|ε|β

M/|ε|β (emu/g)

2.0x103
4.0x103
H/|ε|β+γ

0.0

101

100

T > TC

50

T > TC

0

0.0

100
104

105

2.0x106
4.0x106
H/|ε|β+γ

106

107

T < TC

102

200
T < TC
150
M/|ε|β

101
T > TC

100

T > TC

50
0

100

0.0

104

105

2.0x106
4.0x106
H/|ε|β+γ

106
H/|ε|β+γ

belong to other universality classes (such as the T-MFT and 3D
Ising models) if 1/2 o s o 2, which can be the case taking place
in our samples.
Together with assessing the critical behaviors of La0.7Ca0.3Mn1À xNixO3 samples, we have also considered the magnetic-entropy
change (ΔSm) and its field dependence, as shown in Fig. 6. At a
given temperature for each sample, À ΔSm increases with increasing
H. Around TC, À ΔSm(T) curves reach the maxima, |ΔSmax|. The
|ΔSmax| values determined for x¼0.09, 0.12, and 0.15 in the field
H¼ 40 kOe are about 7.1, 5.2, and 3.4 J kg À 1 K À 1, respectively, which
are smaller than those obtained from the parent compound [7].
Though the Ni doping reduces the |Δ Smax| value, the linewidth

of the À Δ Sm(T) curves become broadened due to the FOMT–
SOMT transformation, enhancing the refrigerant capacity (RC).
Particularly, at TC the H dependences of |Δ Smax| can be well
described by a power law of |Δ Smax| p Hn [24], where values
n ¼0.55, 0.68, and 0.77 for x ¼0.09, 0.12, and 0.15, respectively.
These values are different from those (n ¼0.33, 0.41, and 0.48
for x ¼0.09, 0.12, and 0.15, respectively) calculated from the
relation n ¼1 þ (β À 1)/(β þ γ ) [23]. As shown in Ref. [34], n is
known as a function of T, H and |Δ Sm|, which can also be
obtained from the relation n ¼dln|ΔS m|/dlnH. Depending on the
variation of these parameters, n would be different. It reaches
the minimum at temperatures in the vicinity of T C [23]. We
believe that a large deviation of the n values obtained from two
routes is because the exponent values β and γ determined from
the MAP method are much different from those expected for
the MFT. In other words, La0.7Ca0.3 Mn1 À xNi xO3 samples are not
conventional ferromagnets. There are the magnetic inhomogeneity, and the existence of FOMT and/or SOMT properties
(particularly for two samples with x ¼0.09 and 0.12 lying in the
crossover region). For conventional ferromagnets obeyed the
MFT, n is equal to 2/3. However, experimental results based on
the framework of the SOMT (MFT) theory for inhomogeneous
ferromagnets, like the present cases, introduce the values n
different from 2/3 [23,24].

107

(Oe)

Fig. 5. (Color online) Scaling performance of M/|ε|β versus H/|ε|β þ γ in the log
scale at temperatures T o TC and T 4 TC for La0.7 Ca0.3Mn1 À xNixO3 with (a)

x ¼ 0.09, (b) x ¼ 0.12 and (c) x ¼ 0.15. The insets plot the same data in the
linear scale.

of the FOMT makes of their exponent values different from
those expected for the theoretical models, such as the cases of
La0.7Ca0.3 MnO3 and La0.9 Te0.1MnO 3 [5,31]. With a higher Nidoping content of x ¼0.15, one can see that its β value ( ¼0.320)
is close to that expected for the 3D Ising model (β ¼0.325),
indicating the existence of short-range FM order associated
with the magnetic inhomogeneity, and FM/anti-FM mixed
phase. It comes to our attention that the β value tends to shift
towards the values of the Heisenberg model and MFT if Ni
content (x) in La 0.7Ca0.3 Mn1 À x NixO 3 is higher than 0.15. For
inhomogeneous ferromagnets, the critical values usually
depend on the magnetic field ranges employed for MAP analyses because of a significant field-induced change in the nature
and range of the FM interaction [9,32]. Performing a renormalization group analysis of exchange-interaction systems, Fisher
et al. found the exponent values depending on the range of
exchange interaction characterized by J(r) ¼ 1/r d þ s (where d,
and s are the dimension of the system, and the interaction
range, respectively) [33]. The MFT exponents are valid for s o 1/
2 while the Heisenberg ones are valid for s 4 2. The exponents

4. Conclusions
We studied the critical behavior and related physical properties of manganites La 0.7 Ca 0.3 Mn1 À x Ni x O 3 (x ¼ 0.09, 0.12 and
0.15) around their T C values. Detailed analyses of the M–H–T
data based on the MAP method revealed the stability in value
of γ E 1, demonstrating the real PM behavior above T C in the
samples. However, in the FM region, experimental results
revealed the sample x ¼0.15 undergoing the SOMT. Its β
exponent is close to that expected for the 3D Ising model. For
the samples with lower Ni-doping contents, their exponents β

( ¼ 0.171 and 0.262 for x ¼ 0.09 and 0.12, respectively) indicate
the samples exhibiting tricriticality associated with the FOMT–
SOMT transformation; in which, the FOMT is dominant at the
fields lower than H L . Short-range FM interactions are thus
found in all the samples. Interestingly, around T C , field dependences of |Δ S max | can be described by a power law |Δ S max |
p H n . The n values ( ¼0.55–0.77) obtained from the power-law
fitting are higher than those (n ¼ 0.33–0.48) calculated from the
relation n ¼ 1 þ( β À 1)/(β þ γ ). We believe that the deviation of
the n values obtained from two ways is related to the using of
the approximate MFT (the MAP method) for unconventional
ferromagnets (with the existence of the magnetic inhomogeneity, and FOMT and/or SOMT properties), where the exponent values β and γ determined are much different from those
expected for the MFT.


T.-L. Phan et al. / Solid State Communications 184 (2014) 40–46

45

8

8

6

6

4

4

40 kOe

|ΔSmax| α Hn
(with n = 0.55)

30 kOe

2

2

20 kOe

200

210

220

230

0

10

20

30

40

6

6

4

4
40 kOe

|ΔSmax| α Hn
(with n = 0.68)

30 kOe

2

20 kOe

0
170

2
0

10 kOe

180

190

200

210

|ΔSmax| (Jkg-1K-1)

190

-ΔSm (J.kg-1.K-1)

0

10 kOe

0

0

10

20

30

40

4
3

3
40 kOe

2

2

30 kOe

|ΔSmax| α Hn
(with n = 0.77)

20 kOe

1

1
0

10 kOe

150

160 170

180

190

T (K)

0

10

20

30

40

H (kO e)

Fig. 6. (Color online) À ΔSm(T) curves with the fields H¼ 10, 20, 30 and 40 kOe, and field dependences of |ΔSmax| at TC fitted to a power law |ΔSmax| p Hn for
La0.7Ca0.3Mn1 À xNixO3 with (a, b) x¼ 0.09, (c, d) x¼ 0.12 and (e, f) x ¼ 0.15.

Acknowledgment
This research was supported by the Converging Research
Center Program through the Ministry of Science, ICT and Future
Planning, Korea (2013K000405), and by NAFOSTED of Vietnam
(103.02-2010.38).

References
[1] A.P. Ramirez, J. Phys.: Condens. Matter 9 (1997) 8171.
[2] A.J. Millis, B.I. Shraiman, R. Mueller, Phys. Rev. Lett. 77 (1996) 175.
[3] J. Mira, J. Rivas, L.E. Hueso, F. Rivadulla, M.A. Lopez Quintela, J. Appl. Phys. 91
(2002) 8903.
[4] A. Berger, G. Campillo, P. Vivas, J.E. Pearson, S.D. Bader, E. Baca, P. Prieto,
J. Appl. Phys. 91 (2002) 8393.
[5] H.S. Shin, J.E. Lee, Y.S. Nam, H.L. Ju, C.W. Park, Solid State Commun. 118 (2001)

377.
[6] S. Taran, B.K. Chaudhuri, S. Chatterjee, H.D. Yang, S. Neeleshwar, Y.Y. Chen,
J. Appl. Phys. 98 (2005) 103903.
[7] P. Lampen, N.S. Bingham, M.H. Phan, H. Kim, M. Osofsky, A. Pique, T.L. Phan,
S.C. Yu, H. Srikanth, Appl. Phys. Lett. 102 (2013) 062414.
[8] J. Mira, J. Rivsa, F. Rivadulla, C.V. Vazquez, M.A.L. Quintela, Phys. Rev. B 60
(1999) 2998.
[9] P. Zhang, P. Lampen, T.L. Phan, S.C. Yu, T.D. Thanh, N.H. Dan, V.D. Lam,
H. Srikanth, M.H. Phan, J. Magn. Magn. Mater. 348 (2013) 146.

[10] D.T. Hanh, M.S. Islam, F.A. Khan, D.L. Minh, N. Chau, J. Magn. Magn. Mater. 310
(2007) 2826.
[11] N. Moutis, I. Panagiotopoulos, M. Pissas, D. Niarchos, Phys. Rev. B 59 (1999) 1129.
[12] M.H. Phan, V. Franco, N.S. Bingham, H. Srikanth, N.H. Hur, S.C. Yu, J. Alloys
Compd. 508 (2010) 238.
[13] M.H. Phan, S.B. Tian, S.C. Yu, A.N. Ulyanov, J. Magn. Magn. Mater. 256 (2003)
306.
[14] T.D. Thanh, L.H. Nguyen, D.H. Manh, N.V. Chien, P.T. Phong, N.V. Khiem,
L.V. Hong, N.X. Phuc, Physica B 407 (2012) 145.
[15] S.H. Hua, P.Y. Zhang, H.F. Yang, S.Y. Zhang, H.L. Ge, J. Magn. 18 (2013) 34.
[16] P.J. Lampen, Y.D. Zhang, T.L. Phan, P. Zhang, S.C. Yu, H. Srikanth, M.H. Phan,
J. Appl. Phys. 112 (2012) 113901.
[17] Y.D. Zhang, T.L. Phan, S.C. Yu, J. Appl. Phys. 111 (2012) 07D703.
[18] S. Rößler, U.K. Rößler, K. Nenkov, D. Eckert, S.M. Yusuf, K. Dörr, K.-H. Müller,
Phys. Rev. B 70 (2004) 104417.
[19] L.E. Hueso, P. Sande, D.R. Miguéns, J. Rivas, F. Rivadulla, M.A. López-Quintela,
J. Appl. Phys. 91 (2002) 9943.
[20] A. Arrott, J.E. Noakes, Phys. Rev. Lett. 19 (1967) 786.
[21] H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford
University Press, London, 1971.

[22] S.K. Banerjee, Phys. Lett. 12 (1964) 16.
[23] V. Franco, J.S. Blázquez, A. Conde, Appl. Phys. Lett. 89 (2006) 222512.
[24] H. Oesterreicher, F.T. Parker, J. Appl. Phys. 55 (1984) 4336.
[25] J. Mira, J. Rivas, M. Vazquez, J.M.G. Beneytez, J. Arcas, R.D. Sanchez, M.A.
S. Rodriguez, Phys. Rev. B 59 (1999) 123.
[26] J.M.D. Coey, Magnetism and Magnetic Materials, Cambridge University Press,
New York, 2010.
[27] A. Arrott, Phys. Rev. 108 (1957) 1394.
[28] S. Mukherjee, P. Raychaudhuri, A.K. Nigam, Phys. Rev. B 61 (2000) 8651.


46

T.-L. Phan et al. / Solid State Communications 184 (2014) 40–46

[29] D. Kim, B. Revaz, B.L. Zink, F. Hellman, J.J. Rhyne, J.F. Mitchell, Phys. Rev. Lett. 89
(2002) 227202.
[30] N. Khan, P. Mandal, K. Mydeen, D. Prabhakaran, Phys. Rev. B 85 (2012) 214419.
[31] J. Yang, Y.P. Lee, Y. Li, Phys. Rev. B 76 (2007) 054442.
[32] T.L. Phan, Y.D. Zhang, P. Zhang, T.D. Thanh, S.C. Yu, J. Appl. Phys. 112 (2012)
093906.

[33] M.E. Fisher, S.K. Ma, B.G. Nickel, Phys. Rev. Lett. 29 (1972) 917.
[34] A. Biswas, T.L. Phan, N.H. Dan, P. Zhang, S.C. Yu, H. Srikanth, M.H. Phan, Appl.
Phys. Lett. 103 (2013) 162410.